Thank you for your service.
Neither of my M16 bolt carriers have chrome bolt bores.
Not sure if you mean the bore or the bolt carrier finish, but either way, just a little oil is good. More oil will make no difference except it will capture more residue and turn into soot.
Anderson Arms produces an AR15 with a proprietary "no lube" metal treatment. I ran at least 500 rounds through it totally dry and
degreased, no problem. For other AR's, a puff of remoil after cleaning does it for me.